On my Roamio, it seems that the small preview screen is visible when viewing the guide and/or in TiVo Central. On my Mini, the preview screen is only visible when viewing the guide, NOT in TiVo Central. Is that normal?

Yes, that's normal. The preview screen takes a tuner from the host anytime it is showing on the Mini, so going to TiVo Central from live-tv on the Mini will free up your live-tv tuner for other purposes. That seems quite useful, especially if you have several Minis.

Yes but even when watching a previously recorded show, when you hit the TiVo button the window disappears. I would prefer the Mini to behave like a regular TiVo and keep playing the recorded show or keep playing live TV in the window after hitting the TiVo button. I would like the experience with the Mini to be as close as possible to the experience of using a stand alone TiVo. But unfortunately it isn't because of the behavior of that preview window.

I think it would be more confusing to people if it did work for recordings but not live TV.

If they did add it then it would need to work for both. Wouldn't be a huge deal if they did though since the tuner times out after 90 minutes if there is no remote input. Plus you could still release it instantly if you went into the menu and pressed Slow to close the window.